Geodesic
Periodic Solutions of Periodic Retarded Functional Differential Equations
Marcin Pawłowski1
1 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 4, pp. 353-363

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The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) $x'(t) = f(t, x_{t})$, where $f$ is $T$-periodic in $t$. We construct a pair of subsets of ${\mathbb R} \times {\mathbb R}^{n}$ called a $T$-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a $T$-periodic solution.
DOI : 10.4064/ba52-4-2
Keywords: paper presents geometric method finding periodic solutions retarded functional differential equations rfde where t periodic construct pair subsets mathbb times mathbb called t periodic block compute its lefschetz number nonzero there exists t periodic solution

Marcin Pawłowski 1

1 Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland 
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Marcin Pawłowski. Periodic Solutions of Periodic Retarded Functional Differential Equations. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 4, pp. 353-363. doi: 10.4064/ba52-4-2

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